Efficient Beltrami flow using a short time kernel

Authors:
Alon Spira;Ron Kimmel;Nir Sochen
Affiliations:
Department of Computer Science, Technion, Israel;Department of Computer Science, Technion, Israel;Department of Applied Mathematics, University of Tel-Aviv, Israel
Venue:
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Year:
2003

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Abstract

We introduce a short time kernel for the Beltrami image enhancing flow. The flow is implemented by 'convolving' the image with a space dependent kernel in a similar fashion to the implementation of the heat equation by a convolution with a gaussian kernel. The expression for the kernel shows, yet again, the connection between the Beltrami flow and the Bilateral filter. The kernel is calculated by measuring distances on the image manifold by an efficient variation of the fast marching method. The kernel, thus obtained, can be used for arbitrary large time steps in order to produce adaptive smoothing and/or a new scale-space. We apply it to gray scale and color images to demonstrate its flow like behavior.